Question

find all real numbers x such that 4x-18>2 and -17x -8>-25

Answer 1

\[4x -18>2 and -17 x 8 \ge -25\]

Answer 2

First solve 4x-18>2 and -17x-8>-25 seperately

Answer 3

can you?

Answer 4

i dont really understand the information given

Answer 5

we need to find all real numbers x that satisfies both the inequalities

Answer 6

oh wait i can do that but what do i need to do after i solved the equations separately

Answer 7

take the common region of the both the solutions

Answer 8

Solving is just like solving equations... manipulate the inequality to make it
x > something
or x < something
I'll do one of them, you do the other, all right?

4x - 18 > 2
(You need to get rid of the -18 on the left side)

You add 18 to both sides...
4x - 18 + 18 > 2 + 18

Simplify
4x > 20

Now divide both sides by 4. Since 4 is positive, dividing both sides by 4 WILL NOT change the inequality.
\[\Large \frac{4x}4 > \frac{20}4\]

Simplify
\[\Large\color{blue}{x>5}\]

And you're done solving the first inequality. Now it's your turn, do the second one :)

Answer 9

ok i got \[x \le1\]

Answer 10

Oh, so it has that equal sign then?
Next time, type >= for greater than or equal to and <= for less than or equal to.
I'm sure the folks on OS would understand.
And it's correct :)

Answer 11

So you have
\[\Large \color{blue}{x\ge5}\]
\[\Large \color{red}{x\le1}\]

Answer 12

Can you graph these?
Unless you can visualise them already, of course.

Answer 13

My teacher says... if, say, for graphing \(x\ge5\)

Answer 14

Make sure x is on the LEFT side of the inequality.
Now, if it has the 'or equal to' bit, or it's a \(\ge\) or a \(\le\) symbol, then draw a shaded circle on top of the number in question. In this case 5
And then ...

Answer 15

Draw the arrow in the direction of the arrow where the inequality sign points.
In the case of \(x\ge 5\) it points to the right. So...